My dependent variable is HHI and CR4 index. While treating them in log my results are better. Is there any problem by treating a index value in Log .
Dear Madan Dhanora,
Since you mention a dependent variable, I take it you run a regression. I a regression, you aim at finding a maximum. If you first log transform a variable, find the maximum in logs, and then transform it back, the maximum is (approximately) at the same point as if you had maximized the original variable. This is why you get the correct estimates of coefficients.
When taking logs, extreme values become much less extreme. You run a smaller risk that outliers bias your estimates. This is why taking logs is not only no mistake, but can be desirable.
Do, however, not forget to either transform your results back, or to interpret them properly.
Hope this helps
Christoph Engel
As an index is a numerical data it is easily changed to log. When using log you can make analysis of elasticity that shows the percentual varitation of a variable in relation to another one. For instance, if the coeficient is 0,02 of an independent variable it means that when this variable increases 1%, the dependent one will increase 0,02%. It is useful for assessing the sensibility of a variable to another.
Madan,
I suspect all of the previous answers are correct; however, after I thought about it more and visiting with a highly respected statistician in our Department of Math & Econ, I thought it might be a good idea share some questions and ideas.
First I explained the CR-4 and HHI to my colleague with an example that is in the file attached. Simply, it goes like this:
Firm % of Mkt % of Mkt^2
A 30 900
B 25 625
C 20 400
D 15 225
E 10 100
Total 100 2250
CR-4 = 90 HHI=2250
The questions he asked, are why are you doing the transformation?
Is it to try normalize a positively skewed distribution, for example?
Also, what are your transforming (into logs)? Is it the natural log of CR-4 (i.e., ln90 = 4.5 and/or ln2250=7.72 in this example)? Is it the log of each element in the CR-4 and/or HHI? This seems unlikely; however, it is not clear.
What does it mean when you say:
"My dependent variable is HHI and CR4 index."
Does it mean you tried the model with each separately? Alternatively, are you trying to create your own index, somehow using both the CR-rand HHI at the same time (e.g., in some kind of transformation before taking the logs)?
Once again, the answers by Rivalino, Christoph, Luiz, and Gowkani seem correct in general and are important to remember. Without seeing your actual model or data, I though these questions might ensure we are not missing something.
Rob
One of my independent variable is Assets(%of GDP). While treating it in log my results are better. Is there any problem by treating a percentage value in Log? .
From an empirical experience taking natural log of an index improves results of the model's findings. It is very possible but you need to interpret the findings as percentage change.
I think you have to go beyond the mathematical sense of taking a log of an index. Regardless of the mathematical feasibility and meaning of this log and the mathematical-econometrical relationship between variables... what about the economic meaning of those variables and relationships?
So, I think you have to start with a deep reflexion about the economics (theoretical) meaning of variables and the relationships between them. Once you have undertaken this theoretical review, you will be able to correctly interpret variables and relationships, and then you will find the (economics) answer for your question.
In other words, the purpose of transforming variables or building indexes is to help us to analyse and interpret economic theories, to evaluate economic policies, to make forecasting, etc. Obtaining better estimations results (p-values, r2,...) should not be a target by itself, but only if this improvement in estimation can help us to analyse, interpret, evaluate,... answering our research questions or contrasting our research hypothesis.
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